IMHO if you are going to have an argument about _terminology_ you had better be able to listen to, and understand, different perspectives, rather than simply flat out stating that others are wrong.
This is not physics where ideas are subject to experimental verification; these are words where the meaning is in people's head.
You can explain why different terminology would be better or clearer; and if you do a good job in that explanation you can convince others and change the meaning of the words in their head. But if you simply call people 'snowflakes' they will ignore you.
On the physics: You can clearly define a 180 degree phase difference.
Consider a 2 pole alternator designed with adjustable stator coils, so that you can change the mechanical angle between them. Since there are 360 degrees in a complete rotation you can clearly define 360 degrees of phase relation.
Similarly, in _3_ phase machines we describe the phase angles as 0, 120, and 240 degrees.
Now, in a single frequency pure sine wave situation you cannot distinguish between a true '180' degree phase offset generated by that adjustable alternator and a simple inversion. For purpose of generating a rotating field, such a phase difference (by inversion _or_ 180 degree mechanical rotation) is effectively single phase. Since this simple inversion looks like the 180 degree rotation of the adjustable output, it seems reasonable to use the term 180 degree phase difference.
If you are going to argue that a 180 degree phase difference is meaningless, then I expect you to try to convince the engineering community to describe three phase power using the phase angles 0, 120, 60.
If the adjustable alternator output was somehow not a pure sine wave, then it might be possible to distinguish between the 180 degree rotation of the adjustable coil and a simple inversion.
And just to keep things amusing, in the US, for large residential applications such as apartments, each individual dwelling will be supplied with 2 legs plus neutral of a 208/120 system. This is _called_ single phase because of how it is used, even though there is a real phase difference that can be used to generate a rotating field.
-Jon